To solve this problem, let's go through it step by step.
### Step 1: Calculate the Volume of the Rectangular Prism
First, find the volume of the rectangular prism. The volume [tex]\( V \)[/tex] of a rectangular prism can be found using the formula:
[tex]\[ V = \text{length} \times \text{width} \times \text{height} \][/tex]
Given:
- Length = 6 cm
- Width = 3 cm
- Height = 4 cm
So:
[tex]\[ V = 6 \, \text{cm} \times 3 \, \text{cm} \times 4 \, \text{cm} \][/tex]
[tex]\[ V = 72 \, \text{cm}^3 \][/tex]
### Step 2: Calculate the Volume of a Single Cube
Since the edge length of each cube is 1 cm, the volume [tex]\( v \)[/tex] of one cube is:
[tex]\[ v = \text{edge length}^3 \][/tex]
[tex]\[ v = 1 \, \text{cm} \times 1 \, \text{cm} \times 1 \, \text{cm} \][/tex]
[tex]\[ v = 1 \, \text{cm}^3 \][/tex]
### Step 3: Calculate the Number of Cubes Needed to Fill the Rectangular Prism
To find the number of cubes needed, divide the volume of the rectangular prism by the volume of one cube:
[tex]\[ \text{Number of cubes} = \frac{\text{Volume of the rectangular prism}}{\text{Volume of one cube}} \][/tex]
Using the volumes we calculated:
[tex]\[ \text{Number of cubes} = \frac{72 \, \text{cm}^3}{1 \, \text{cm}^3} \][/tex]
[tex]\[ \text{Number of cubes} = 72 \][/tex]
### Conclusion
To fill the rectangular prism, 72 cubes are needed.
